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#1
03-23-2004, 07:03 AM
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ranking hands against \"push hands\" preflop
Most people are familiar with the following way of ranking hands:
http://www.jazbo.com/poker/huholdem.html which is win percentage against a random hand. Problem is, most people don't play random hands. They play select hands. If instead of computing these numbers against a random hand, we compute them against typical "push" hands: say any pair, or any ace, how does the list change? What hands have positive expectation against a random hand that is any pair or any ace? I did a calculation, and came up with these numbers: Gah! I can't get netscape to paste these damn numbers in. I'll post tomorrow. Anyone want to hazard a guess at what hands have +EV against any pair or any ace? Also, I want to double-check how I did the calculation. I tried to take into account the probability that your opponent holds hand X given your hole cards Y, since some possibilities are "blocked" by your holdinds. Details to come. eastbay 
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#2
03-23-2004, 03:21 PM
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Re: ranking hands against \"push hands\" preflop
From the top of my head:
I would guess that the win% of the top hands in jazbo's list will improve dramatically, while the bottom hands will lose much value. Pairs lower than 77 will lose some value, Aces with 7 kicker and below will lose value dramatically, while medium and med-high connectors will somewhat improve. For example: in their list, 55 is little better than QJs. I would say that in your list, QJs will stand better. Is this even close?
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#3
03-25-2004, 12:12 PM
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Re: ranking hands against \"push hands\" preflop
[ QUOTE ]
From the top of my head: I would guess that the win% of the top hands in jazbo's list will improve dramatically, while the bottom hands will lose much value. Pairs lower than 77 will lose some value, Aces with 7 kicker and below will lose value dramatically, while medium and med-high connectors will somewhat improve. For example: in their list, 55 is little better than QJs. I would say that in your list, QJs will stand better. Is this even close? [/ QUOTE ] Draw your own conclusions from the results I just posted. I'd say you hit some ideas correctly and missed a little with others. eastbay
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#5
03-25-2004, 12:08 PM
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Results are in
Ok, here's the results I'm getting when comparing against the "any pair, any ace" set of hands. These are win fractions.
AAo: 0.868701 KKo: 0.717437 QQo: 0.694589 JJo: 0.671537 TTo: 0.648316 AKs: 0.633812 99o: 0.618106 AKo: 0.615742 AQs: 0.602706 88o: 0.594209 AQo: 0.582691 AJs: 0.570817 77o: 0.568266 AJo: 0.548738 66o: 0.543522 ATs: 0.539245 55o: 0.518897 ATo: 0.515079 A9s: 0.498569 44o: 0.489243 A9o: 0.471471 A8s: 0.468405 33o: 0.45922 A8o: 0.439287 A7s: 0.439104 JTs: 0.435095 QJs: 0.432201 KQs: 0.429669 QTs: 0.428981 22o: 0.428917 KJs: 0.426322 KTs: 0.423085 T9s: 0.421997 J9s: 0.41557 A6s: 0.412231 98s: 0.410088 Q9s: 0.409378 A7o: 0.407937 T8s: 0.407644 A5s: 0.406675 JTo: 0.403909 K9s: 0.40339 87s: 0.401158 J8s: 0.401144 QJo: 0.400481 KQo: 0.397427 QTo: 0.39714 97s: 0.395388 Q8s: 0.394819 KJo: 0.393954 T7s: 0.392131 A4s: 0.391515 76s: 0.390746 KTo: 0.390595 T9o: 0.390155 K8s: 0.38856 86s: 0.386708 K7s: 0.385625 J7s: 0.385609 J9o: 0.383063 A3s: 0.381557 96s: 0.380882 K6s: 0.380852 Q7s: 0.379169 A6o: 0.379119 65s: 0.377947 98o: 0.377458 T6s: 0.377398 Q6s: 0.377175 Q9o: 0.376213 T8o: 0.374833 A5o: 0.373404 K5s: 0.372262 75s: 0.372141 A2s: 0.371275 J6s: 0.37076 K9o: 0.369575 Q5s: 0.368592 87o: 0.368155 85s: 0.36804 J8o: 0.367665 54s: 0.365187 J5s: 0.364974 K4s: 0.364348 95s: 0.362213 97o: 0.361791 Q8o: 0.360678 Q4s: 0.360674 64s: 0.359884 T5s: 0.35859 T7o: 0.358288 76o: 0.357173 A4o: 0.357137 J4s: 0.357052 K3s: 0.356324 74s: 0.353963 K8o: 0.35376 T4s: 0.353475 86o: 0.352724 Q3s: 0.352646 J7o: 0.351098 K7o: 0.350695 84s: 0.349813 J3s: 0.34902 K2s: 0.348201 53s: 0.346731 A3o: 0.346479 96o: 0.346298 K6o: 0.345598 T3s: 0.345439 Q2s: 0.344518 Q7o: 0.343993 94s: 0.34389 65o: 0.343729 T6o: 0.34255 Q6o: 0.3419 63s: 0.341299 J2s: 0.340887 93s: 0.33867 43s: 0.33766 75o: 0.337437 T2s: 0.337301 K5o: 0.336543 73s: 0.335466 A2o: 0.335453 J6o: 0.335241 85o: 0.33291 Q5o: 0.332851 83s: 0.331219 92s: 0.330518 54o: 0.330241 J5o: 0.329216 K4o: 0.328023 52s: 0.327759 95o: 0.326483 82s: 0.325903 64o: 0.324395 Q4o: 0.324329 T5o: 0.322591 62s: 0.322283 J4o: 0.320689 K3o: 0.319379 42s: 0.318872 74o: 0.31797 T4o: 0.317097 72s: 0.316582 Q3o: 0.315681 84o: 0.313391 J3o: 0.312037 K2o: 0.310618 53o: 0.310492 32s: 0.309713 T3o: 0.308441 Q2o: 0.306915 94o: 0.306866 63o: 0.304498 J2o: 0.303267 93o: 0.301252 43o: 0.3009 T2o: 0.299667 73o: 0.298163 83o: 0.293484 92o: 0.292463 52o: 0.290183 82o: 0.287756 62o: 0.284141 42o: 0.280797 72o: 0.277943 32o: 0.271115 Some notes: * good pairs and aces increase in rank vs. other pairs and aces, due to the "domination" effect. * There aren't many hands which have a win pct > 50% against a random pair or ace! The only "winners" are: AAo, KKo, QQo, JJo, TTo, AKs, 99o, AKo, AQs, 88o, AQo, AJs, 77o, AJo, 66o, ATs, 55o, ATo * If you want an edge of 70% or better, you have to wait for KK or AA. * The best hand other than an ace or pair is JTs! Maybe that old idea about JT being the "best hand" wasn't _so_ crazy. * Note the abysmal rank of A2o, which some guy at the aviation club came over the top all-in with last night on WPT... to lose. * Fossilman's semi-famous T9s play isn't far from as good as you can do if you don't have an ace or pair in front of you. Higher suited connectors are better, but not by much. * T8s ranks better than A5s! Beware dominated aces! Here's a side-by-side on the top 15 hands in each case: vs. As, pairs vs. random hand -------------|---------------| AAo: 0.868701 AAo: 0.852037 KKo: 0.717437 KKo: 0.823957 QQo: 0.694589 QQo: 0.799252 JJo: 0.671537 JJo: 0.774695 TTo: 0.648316 TTo: 0.750118 AKs: 0.633812 99o: 0.720573 99o: 0.618106 88o: 0.69163 AKo: 0.615742 AKs: 0.670446 AQs: 0.602706 77o: 0.66236 88o: 0.594209 AQs: 0.662089 AQo: 0.582691 AJs: 0.653927 AJs: 0.570817 AKo: 0.65318 77o: 0.568266 ATs: 0.646024 AJo: 0.548738 AQo: 0.644298 66o: 0.543522 AJo: 0.635612 Note how much AKo jumps up. Also note that AJs goes down in rank, but AJo goes up! Comments welcome! eastbay
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#6
03-25-2004, 12:21 PM
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Re: Results are in
Interesting. I think the biggest surprise to me was how high JTs ranked, at least relative to KQs, QJs, KJs.
Keep in mind that as the table gets down to 2 or 3 players people will push with hands other than pairs and aces, which will change these odds around a fair bit.
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#7
03-25-2004, 06:38 PM
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Re: Results are in
Very interesting
I think these rankings paint a far more accurate picture of what hands are good calling hands. How hard would it be for you to rank vs a random chance of a slightly more refined list of possible opposition hands I'd actually like to take some hands like A2o-A6o off the list and add some hands like KQ, KJ, and suited broadway cards Also, does this list take into account the greater likelihood that your opponent is holding AK than a pair, etc... [ QUOTE ] * There aren't many hands which have a win pct > 50% against a random pair or ace! The only "winners" are: AAo, KKo, QQo, JJo, TTo, AKs, 99o, AKo, AQs, 88o, AQo, AJs, 77o, AJo, 66o, ATs, 55o, ATo [/ QUOTE ] This is a very powerful point. I think that this point almost comes close to a suggested calling requirement against shortstacks pushing on the bubble Good Post Brad S
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#8
03-25-2004, 11:02 PM
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Re: Results are in
[ QUOTE ]
Very interesting I think these rankings paint a far more accurate picture of what hands are good calling hands. How hard would it be for you to rank vs a random chance of a slightly more refined list of possible opposition hands I'd actually like to take some hands like A2o-A6o off the list and add some hands like KQ, KJ, and suited broadway cards [/ QUOTE ] Dirt simple. Give me any list, I'll give you the rankings. [ QUOTE ] Also, does this list take into account the greater likelihood that your opponent is holding AK than a pair, etc... [/ QUOTE ] Yes it does. This was slightly tricky to get right and there's still one point which seems "wrong" to me but it's the only way I can the probabilities to sum to unity (which is of course a necessary condition for it to be correct) Here's the case I'm confused by: when you hold an offsuit non-pair hand and your opponent holds a suited hand that matches both of your cards in rank, how many different hands can he be holding? [ QUOTE ] [ QUOTE ] * There aren't many hands which have a win pct > 50% against a random pair or ace! The only "winners" are: AAo, KKo, QQo, JJo, TTo, AKs, 99o, AKo, AQs, 88o, AQo, AJs, 77o, AJo, 66o, ATs, 55o, ATo [/ QUOTE ] This is a very powerful point. I think that this point almost comes close to a suggested calling requirement against shortstacks pushing on the bubble Good Post Brad S [/ QUOTE ] Thanks. Glad you got something out of it. eastbay
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#9
03-26-2004, 04:31 AM
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Re: Results are in
[ QUOTE ]
Here's the case I'm confused by: when you hold an offsuit non-pair hand and your opponent holds a suited hand that matches both of your cards in rank, how many different hands can he be holding? [/ QUOTE ] You mean if you hold AKo how many ways can someone hold AKs? The answer is 2 Great work btw, some interesting info there.
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#10
03-26-2004, 11:36 AM
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Re: Results are in
[ QUOTE ]
You mean if you hold AKo how many ways can someone hold AKs? The answer is 2 Great work btw, some interesting info there. [/ QUOTE ] Well temper your praise, because I made a mistake somewhere. For the "you hold offsuit cards" case I get a total of 1224 possible opponent's hands unless I make that number 3 instead of 2. So here's the cases I'm considering, using AKo as an example: You hold AKo. How many AKs can your opponent hold? 2. How many AKo can your opponent hold? How many AA? How many KK? How many Axs? How many Kxs? How many Axo? How many Kxo? Is there some other case which is not the usual 6, 4, 12 for pair, suited, offsuit that I'm forgetting? eastbay
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Hybrid Mode
